Math problem for the mentally curiousFor those who enjoy a math problem to finish off a great day on this planet, here is a problem for you. I randomly came up with it while watching the democratic debate last night (must have been bored). It is two problems, the second one follows from the first.
Problem statement!Suppose you owe me money from a recent lone. Your unfortunate situation lets me demand money from you in either one of two ways. You get the choice to choose one of them .
Option 1:You pay me 1 dollar a day for $$n$$ days.
Option 2.You pay me 0 cents today (day 1), 1 cent tomorrow (day 2), $$0+1+2$$ cents on day 3, $$0 + 1 + \dots + i + \dots +(n-1)$$ cents on day n.
The dilemma:: At what day does it become not profitable for you to pay me with option two.
: Additionally, create an expression to tell me how much money I will profit if you pick option 2. Hint: Negative profits for days 1 and so on, are possible until the day when statement 1 above is true.